Vibrating string reference apparatus



Filed June 15,. 1967 ATTORNEY Nov. 10, 1970 R o 5 l mf 13530: H mESBQMmQ A m m 8m m 3 m V moZJzoozwo A m l GPEJDQOZ I. l. w o M o A 3 S Y mm EEEE mN mm(\ 5.55m .v 009 5 c: l| 5243028 2 A o Ila v m n Nm mokjaoosmo 2 8 2 N. a J

United States Patent Oihce 3,538,774 Patented Nov. 10, 1970 3 538 774 VIBRA'IING STRINGREI ERENCE APPARATUS William H. Quick, La Mirada, Calif., assignor to North American Rockwell Corporation, a corporation of Delaware Filed June 15, 1967, Ser. No. 646,240 Int. Cl. G01p 9/04 U.S. Cl. 73-505 19 Claims ABSTRACT OF THE DISCLOSURE A string which is secured between fixed end supports is driven laterally in a first direction by an oscillator coupled to a first pair of electrostatic drive plates. A second pair of electrostatic plates are arranged substantially perpendicular to the first pair to provide a signal which varies as a function of the motion of the string in a direction perpendicular to the first direction. The signal is separated into a first component due to the string vibrating in an elliptical path and a second component due to the direction of vibration of the string being displaced from the first direction. A negative feedback loop is utilized to feed the first component back to the second pair of plates to squash the elliptical path and an oscillation loop is utilized to feed the second component back to the second pair of plates to compensate for the tipping of the plane of vibration.

BACKGROUND *OF THE INVENTION 1.Field of the invention The present invention relates to vibrating string reference apparatus and, more particularly, to a method and means for minimizing the precession of the plane of vibration in a vibrating string gyro.

2.Description of prior art It has been demonstrated previously that a vibrating string may operate to provide an angular reference. The general theory of operation is explained more fully in my article entitled Theory of the Vibrating String as an Angular Motion Sensor, Journal of Applied Mechanics, September, 1964, volume 31, No. 3, pp. 523434. The approach is based on using the linear momentum of a vibrating string rather than the angular momentum of a rotating wheel. If the structure supporting the string is allowed to turn about the axis of the string, the plane of the string vibration tends to remain stationary in inertial space, although the string itself rotates with the supports. Thus, the vibrating string provides an inertial angular reference in a manner analogous to the Foucault pendulum. In both, the energy of the stored angular information is periodically interchanged between the potential energy associated with a position vector and the kinetic energy associated with a momentum vector. A means for sensing the angular displacement between the string plane and the supporting structure completes the elements necessary for a position gyroscope.

In order for a vibrating string to effectively operate as a position gyro, the plane of vibration of the string must remain substantially fixed in inertial space as the supporting structure rotates. If an ideal string were obtainable, there would be no tendency for the plane of vibration to precess. An ideal string is one with negligible bending moments and a uniform, circular cross-section. However, with a practical string, neither one of these requirements can be met. No matter how thin an actual fiber may be, there will be a region near its end attachments Where bending moments become important, because of the high bending curvature at these points. This bending may be accounted for by assuming an effective end pivot attachment at the intersection of the undeflected string axis and a tangent to the string near its end (but outside the region of the important bending moments). The crucial point is that, because of elastic anisotropy and/ or geometrical asymmetry, the location of this intersection can vary With the plane of string vibration, giving different lengths to the equivalent ideal string, for different planes of vibration. In other words, this end-fastening elastic asymmetry (anisoelasticity) results in.the vibrating string having a different natural frequency depending upon the plane of vibration. The direction of the maximum natural frequency is generally called the first principle elastic axis and the direction of the minimum natural frequency is generally called the second principle elastic axis. When the string is placed into vibration, there is a. tendency, depending on the type of drive, for the string to swing around into either the first or second principle elastic axis.

Anisoelastic drift is, by a large margin, the dominant precession effect in a vibrating string gyro. Even with a high quality string, if operation is not near optimum conditions, drift rates on the order of one million degrees per hour are easily observed.

It can be shown that end-fastening anisoelasticity does not directly cause the string plane to precess. Rather, through the operation of a cross spring effect, the anisoelasticity causes the string orbit to build up into elliptical motion. This elliptical motion, together with a restoring force which is not linearly proportional to deflection, is the direct cause of orbit precession, which constitutes drift in the gyro sense. This non-linear restoring force is due to the variation in the tension of the string as the string vibrates. As the string moves out, the restoring force is proportional to the deflection multiplied by the tension. As long as the tension remains constant, the restoring force is proportional to the deflection. But in the presence of vibration the tension increases as the string moves out from the central position so that the restoring force is no longer directly proportional to the deflection. The derivation of these relationships is set forth more fully in Theory of the Vibrating String as an Angular Motion Sensor, supra.

As stated above, the anisoelastic effect is the primary cause of elliptical motion which, in the presence of a nonlinear restoring force, causes precession of the plane of vibration of the string. Numerous techniques have been employed in the past to eliminate the precession of the plane of vibration in a vibrating string gyro. In US. patent application Ser. No. 401,177, entitled Rotated Vibrating Whisker Gyro, filed Oct. 2, 1964 by Frederick W. Hauf and William H. Quick, and asigned to North American Aviation, Inc, the assignee of the present invention, there is disclosed a vibrating Whisker gyro in which the whisker is spun rapidly at the same time that it is vibrating. The rotation is at such a rate that the end-fastening bending effect averages out over a short period so that the anisoelastic effect is minimized.

Another system for minimizing the precession of the plane of vibration in a vibrating string gyro is disclosed in US. Pat. No. 3,106,847, entitled Gyroscopic Apparatus, issued Oct. 15, 1963 to W. D. Mullins, In, et al. In that patent, one end of the vibrating string is attached to a disc which resonates to drive the string. At least one electrostatic plate is provided to pick off the motion of the disc so as to provide a signal to drive the disc, thereby creating a self-oscillating loop. With such a configuration, the nonlinear restoring force may be eliminated by operating the longitudinal drive at the proper amplitude. By this, it is meant that if the axial drive is operated with the proper amplitude, the tension of the string may be kept constant. As a result, even though the ellipse will still form due to the anisoelastic effect, the string plane will not precess since the nonlinear restoring force has been eliminated.

Most prior art attempts to minimize precession in a vibrating string gyro have been in the direction of sophisticated systems to drive the string axially at the critical amplitude. Although, generally, such schemes are eifective to minimize precession, the result is obtained through a configuration which is mechanically complex because of the necessity of having a resonating disc to drive the string axially.

If an axial drive is avoided in favor of a lateral drive, still other problems exist. A lateral drive typically consists of a member located adjacent to the string for applying a force to the string to drive it in a direction perpendicular to the axis of the string. In such a configuration, the drive member is usually attached to the supporting case. As a result, when the case rotates, the drive member rotates and this tends to coerce the plane of vibration to follow the case. This is a form of precession which is undesirable in a position gyro.

SUMMARY OF THE INVENTION According to the present invention, an entirely unique approach to the problem of eliminating the precession of the plane of vibration in a vibrating string gyro is undertaken. As stated previously, the primary cause of precession is the elliptical motion of the string in the presence of a non-linear restoring force. Previous attempts to reduce precession have focused on eliminating the non-linear restoring force. However, according to the present invention, the tendency to precess is reduced by eliminating the elliptical motion.

According to the present invention, there is provided a string which is secured between fixed end supports. The string is driven laterally in a first direction utilizing a first pair of electrostatic plates in conjunction with a bridge circuit which is operative to provide a signal which is proportional to the position of the string. This signal is then fed back to the first pair of plates to form a selfoscillating loop. A second pair of electrostatic plates are arranged substantially perpendicular to the first pair to sense motion of the string in a direction perpendicular to the first direction. Through a second bridge network coupled to the second pair of plates, a signal is derived which is proportional to this motion. This signal is separated into a first component due to the string vibrating in an elliptical path and a second component due to the direction of vibration of the string being displaced from the first direction. The first component is applied, via a negative feedback network, back to the second pair of plates to squash the ellipse. The second component is also applied back to the second pair of plates to drive the string so that the vector sum of the drives at the first and second pairs of plates coincides with the plane of vibration of the string.

OBJECTS It is therefore an object of the present invention to provide a novel vibrating string reference apparatus.

It is a further object of the present invention to provide a vibrating string reference apparatus which minimizes the tendency for the plane of vibration to precess.

It is still a further object of the present invention to minimize drift in a vibrating string gyro.

It is another object of the present invention to provide a method and means for eliminating the elliptical motion in a vibrating string gyro.

It is still another object of the present invention to provide a vibrating string gyro which is driven laterally by electrostatic forces.

Another object of the present invention is the provision of laterally driven vibrating string gyro which includes means for causing the direction of the drive to follow the plane of vibration.

Still other objects, features and attendant advantages of the present invention will become apparent to those skilled in the art from a reading of the following description of a preferred embodiment constructed in accordance therewith, taken in conjunction with the accompanying drawings wherein:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a schematic representation, partially in block diagram form, of the preferred embodiment of the present invention; and

FIG. 2 is an end view of the vibrating string of FIG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to the drawings and, more particularly, to FIG. 1 thereof, there is shown a preferred embodiment of the present invention. The stable element of the present inertial reference apparatus consists of an electrically grounded string 1 vibrating in its second mode. A first pair of electrostatic plates, consisting of plates 2 and 3, are arranged parallel to each other and on opposite sides of string 1. A second pair of electrostatic plates, consisting of plates 4 and 5, are arranged parallel to each other and on opposite sides of string 1. Plates 4 and 5 are rotated substantially with respect to plates 2 and 3. The vibration of string 1 in the second mode and the fact that plates 25 are only approximately half as long as string 1 are matters of choice in design. However, since all parts of string 1 move in phase synchronism with each other, the fact that plates 2, 3 and 4, 5 are on separate vibration loops does not effect the outputs.

The plane of vibration of string 1 is generally vertical so that the elements of string 1 move parallel to plates 4 and 5 and perpendicular to plates 2 and 3'. The capacitance from plates 2 and 3 to the grounded string varies cyclically with the motion of string 1. Therefore, in order to cause string 1 to oscillate, it may be made a part of a self-oscillating loop. As shown in FIG. 1, the oscillation loop consists of a primary winding 6 of a transformer 7 connected via a pair of capacitors 8 and 9 to plates 2 and 3. This provides a balanced arrangement in which the current through winding 6 will be balanced in the absence of motion -of string 1. However, as string 1 vibrates and moves between plates 2 and 3, there will be more current through the plate which is closest to string 1. This will unbalance the bridge so as to generate through winding 6 a signal which is proportional to the position of string 1. A secondary 10 of transformer 7 is utilized to pick off this signal which is then amplified by an amplifier 11. The output of amplifier 11 is applied to a demodulator 12 which receives, as its second input, a signal E derived from a carrier generator 13, whose function will be explained more fully hereinafter. Sufiice it to say that the signal at the output of amplifier 11 is the high frequency signal provided by generator 13, modulated by a signal which varies as a function of the motion of string 1. Therefore, demodulator 12 is operative to cancel the frequency component due to carrier generator 13 so as to provide at its output a signal S which is proportional to the motion of string 1. The phase of E applied to demodulator 12 will be selected so as to maximize the sensitivity to string motion. The output of demodulator 12 is applied to a 90 phase shifter 14 whose output S is coupled via a winding 15 of a transformer 16 to the center tap of winding 6. Phase shifter 14 is provided because the output of demodulator 12 is proportional to the position of string 1 whereas the force which must be applied to string 1 in order to sustain oscillations must be in phase with the velocity of the string elements. In other words, phase shifter 14 operates as a differentiating network to convert the signal in phase with position to a signal in phase with velocity.

In order for the foregoing apparatus to operate as a self-oscillating loop, equal and opposite D.C. biases are applied to plates 2 and 3. The biases are shown as being provided by a D.C. amplifier 17 which is operative to provide at its output terminals equal and opposite D.C. voltages which are applied, via a pair of resistors 18 and 19, to plates 2 and 3. With equal and opposite D.C. voltages on plates 2 and 3, string 1 will be attracted to each plate by the same amount since the attractive force is insensitive to the sign of a D.C. signal. However, the signal from phase shifter 14 is applied to winding 6 so as to simultaneously add to both of the D.C. bias signals. Since the same signal is applied to both legs via capacitors 8 and 9 and since the D.C. biases are opposite in sign, the AC. signal from phase shifter 14 is operative to increase the bias at plate 2 while decreasing the bias at plate 3 and vice versa. Also, since the signal from phase shifter 14 is in phase with the velocity of string 1, it will tend to keep string 1 oscillating.

Carrier generator 13 is provided as a source of high frequency excitation. The output E of carrier generator 13 is applied to a winding 20 of transformer 16 and then via windings 15 and '16 and capacitors 8 and 9 to plates 2 and 3. As stated above, the motion of string 1 is operative to modulate E as a function thereof. It is this modulated signal which is sensed by winding 14) and applied to demodulator 12 wherein the E component is eliminated to provide S After differentiation in phase shifter 14, S is applied to winding 15 of transformer 16 where it is added to the carrier signal provided by generator 13. In this manner, the signal sensed by winding as a function of the motion of string 1 is insensitive to the drive voltage being applied to plates 2 and 3. Other techniques for isolating drive and sensing signals will be obvious to those skilled in the art.

Capacitors 8 and 9 are provided so as to isolate the D.C. signals at the outputs of amplifier 17 from the remainder of the drive loop. Similarly, resistors 18 and 19 are provided so as to isolate the high frequency signal at the output of carrier generator 13 from the output of D.C. amplifier 17.

It should be noted that string -1 will vibrate at that frequency at which the loop gain has 0 phase shift and at an amplitude at which the loop gain is unity. It should also be noted that the outputs of demodulator 12 and phase shifter 14 are signals whose frequencies are equal to the frequency of vibration of string 1 and whose amplitudes are proportional to the amplitude of vibration of string 1. Therefore, in order to control and stabilize the amplitude of vibration of string 1, the output of phase shifter 14 or demodulator 12 may be used to control the D.C. biases provided by amplifier 17 As shown in FIG. 1, this may be done by coupling the output of phase shifter 14 to a diode Zll operating as a half wave rectifier. The signal from diode 21 is applied to a resistor-capacitor combination, shown as consisting of a resistor 22 and a capacitor 23, operating as a filter circuit so as to supply to a first input of amplifier 17 a D.C. signal which is proportional to the amplitude of vibration of string 1. A second input to amplifier 17 is provided by a variable source of reference potential. D.C. amplifier 17 is operative to sense the difference between the reference potential and the potential across capacitor 23 to provide D.C. output voltages to plates 2 and 3 as a function thereof.

With a drive circuit as shown in FIG. 1, string 1 will be caused to vibrate in an essentially vertical plane. In the absence of coercive effects, and if string 1 were ideal, the plane of vibration of string 1 would tend to remain stationary in inertial space. However, since string 1 cannot be made infinitely thin and cannot be caused to pivot at its ends like a sine wave, there will be a tendency for the plane of vibration of string 1 to precess towards its first principal elastic axis. The presence of end-fastening anisoelasticity will cause the string orbit to build up into elliptical motion, in the presence of a nonlinear restoring force due to the variation in the tension of string 1 as it vibrates, directly causes orbit precession.

According to the present invention, the tendency of the plane of vibration of string 1 to precess is minimized by effectively eliminating the tendency of string l1 to build up into elliptical motion. Referring again to FIG. 1, plates 4 and 5 are positioned substantially perpendicular to plates 2 and 3 so as to sense motion of string 1 in a direction perpendicular to the drive direction. Plates 4 and 5 are connected via resistors 24 and 25, respectively, to equal and opposite D.C. voltages for the purpose of providing bias as was the case with plates 2 and 3. The D.C. biases for plates 4 and 5 may be independently provided or may be derived from the outputs of D.C. amplifier 17. As was the case with plates 2 and 3, plates 4 and 5 are coupled together by a pair of capacitors 26 and 27 and a winding 28 of a transformer 29, and are excited by the signal E from carrier generator 13. In this manner, a balanced bridge arrangement is provided wherein the signal through winding 28 is E modulated as a function of the position of string 1 with respect to plates 4 and 5. By using a secondary 30 of transformer 29, this position signal can be extracted and fed to an amplifier 31. The output of amplifier 31 is applied to a demodulator 32 which receives, as its second input, the excitation signal E from carrier generator 13. The function of demodulator 32 is to remove E from the output of amplifier 31 and, therefore, the phase of the carrier input signal is chosen appropriately.

The output of demodulator 32, denoted L, is a signal which indicates the motion of string '1 in a direction perpendicular to plates 4 and 5. However, signal L consists of two components. A first component is due to the tipping of the plane of vibration, denoted I. A second component is due to string 1 building up an elliptical motion and is, therefore, proportional to the ellipse thickness, denoted Q. The relationship between these two signal components can be seen from FIG. 2 which shows an end view of string 1. In FIG. 2, it is assumed that there is both a tipping of the plane of vibration and the formation of an ellipse.

Referring again to FIG. 1, in order to derive the portion of signal L which is proportional to the ellipse thickness Q, the output of demodulator 32 is applied, via an amplifier 33, to a demodulator 34. Demodulator 34 is operative to separate the quadrature component Q from signal L by demodulating signal L with a signal which is out of phase with the motion of string 1. In order to do this, demodulator 34 receives, as its second input, a signal from the drive loop, and, more specifically, the signal S derived from phase shifter (14. Since the output of phase shifter 14 is 90 out of phase with the string motion, the output of demodulator 34 will be the quadrature component Q proportional to the ellipse thickness. If, simultaneously with the presence of an ellipse thickness, there is also a tipping of the major axis of the ellipse, demodulator 34 will reject this portion of signal L. In this manner, the output Q of demodulator 34 is a D.C. signal which varies as a function of the ellipse thickness. In order to eliminate the ellipse, the Q signal is applied to a modulator 35 which receives, as its second input, the signal S from the output of demodulator 12. The output of modulator 35 is applied to a gain element 36 and then via a summing element 37 and a winding 38 of a transformer 39 back to plates 4 and 5. The purpose of gain element 36 is to insure that the feedback loop from winding 30 back to plates 4 and 5 has heavy negative gain. By so doing, any elliptical motion of string 1 will result in an error signal which is fed back to plates 4 and 5 to tend to squash the ellipse. In other words, by using a negative feedback circuit, an ellipse is prevented from forming with the exception of the residual amount of ellipticity needed to produce an error signal.

The phase of the signal input for modulator 35 is chosen so that the signal applied to string 1 is in phase with the string motion. The drive signal from gain element 36 is applied to plates 4 and 5 in the same manner as was described with respect to the drive for plates 2 and 3. In

other words, the signal from gain element 36 is applied to winding 38 of transformer 39 which has a second winding 43 for receiving the high frequency carrier from generator 13. Therefore, the negative feedback signal is added to the E carrier and applied to winding 28 of transformer 29 to alternately add to and subtract from the DC. biases on plates 4 and 5.

One other feature of the present invention needs to be discussed. With the present invention, string 1 is being driven laterally between plates 2 and 3 which are fixedly secured to a supporting case, not shown. If the case tips, and the plane of vibration remains fixed, it can be seen that string 1 will be driven in a direction which is not parallel to its plane of vibration. As a result, the drive tends to cause the plane of vibration of string 1 to rotate towards the driving axis which is perpendicular to plates 2 and 3. Because the resonant factor of the oscillator can be made quite large, the required drive is small, and the tendency to coerce the plane is not relatively great. Nevertheless, there will still be some tendency on the part of the plane of vibration to rotate toward the drive axis. In order to counteract this, a compensation is provided to drive string 1 so that the drive follows string 1 rather than the case. T describe this in another way, when string 1 has rotated from its normal null position, the drive tends to coerce string 1 back to its null plane while the drive bias compensation, to be explained hereafter, torques string 1 by an equal and opposite amount. The drive bias compensation is accomplished in the following manner.

As stated previously, the output L of demodulator 32 contains components which are proportional to the tipping of the plane of vibration I and the ellipse thickness Q. Demodulator 34 is operative to demodulate the L signal so as to derive the quadrature component Q. Another demodulator 40 is provided, responsive to the output of amplifier 33, to derive the component of L which is in phase with the motion of string 1. This is accomplished by providing demodulator 40 with a reference signal from the output of demodulator 12 which is in phase with the string motion. Therefore, the output of demodulator 40 is the signal I which represents the tipping of the plane of vibration of string 1 with respect to the reference axis defined by plates 2 and 3. It might be pointed out that the I signal, representing the tipping of the major axis of the ellipse, is the basic gyro output signal which may be utilized to measure the rotation of the case of the gyro in inertial space. The I signal is a DC. signal which is applied to a modulator 41 which receives, as its second input, the signal S from 90 phase shifter 14. The output of modulator 41 is applied to a variable gain circuit 42 whose output is applied, via summing element 37 and windings 38 and 28, to plates 4 and 5. The phase of the reference signal for modulator 41 is chosen so that the signal applied to plates 4 and is in phase with the string velocity.

The requirement for the drive compensation loop can be explained in the following fashion. The ratio of the drive at plates 4 and 5 to the drive at plates 2 and 3 should be equal to the string plane offset angle. The ratio of the cross axis signal to the drive axis signal is also equal to the string plane angle. Thus, the proper drive bias compensation occurs when the total loop gain of the drive compensation loop is the same as that of the self-oscillator loop, namely, unity. In order to control the gain of the drive bias compensation loop, variable gain circuit 42 is provided. In practice, the final adjustment of the gain of circuit 42 is made by operating both loops and setting the gain while observing the output I of the gyro as it is rotated about its input axis.

The effect of the three loops shown in FIG. 1 may be summarized in the following fashion. The force applied between plates 2 and 3 is that necessary to maintain string amplitude by compensating for damping losses. When the string plane rotates from its nominal axis, the normal drive at plates 2 and 3 applies a force component which tends to rotate string 1 towards null. The drive bias compensation provided by the loop including demodulator 40, modulator 41 and variable gain circuit 42 tends to compensate for this effect. At the same time, the anisoelastic effects within string 1 which produce a lateral force tending to cause string 1 to move along an elliptical path, are

compensated for by the loop consisting of demodulator' 34, modulator 35 and gain element 36 which substantially cancel this force. The thickness is minimized by utilizing high gain, negative feedback in the anisoelastic bias compensation loop.

It can, therefore, be seen that in accordance with the present invention there is provided a vibrating string reference apparatus which represents a great simplification over known arrangements. The mechanically complex and expensive drive mechanism for driving the string axially at the critical amplitude is completely eliminated. In its place is substituted a string which is fixedly supported at opposite ends thereof together with two pairs of sensing and driving plates. The string and the case may be made entirely of fused silica which is relatively easy to make. The features of conventional gyros which generally lead to being costly and failure prone will be totally absent, such as precision ball bearings, drive motors, gimbals, output axis bearings, torquing coils, dissimilar materials and flotation fluids with associated seals.

While the invention has been described with respect to a preferred physical embodiment constructed in accordance therewith, it will be apparent to those skilled in the art that various modifications and improvements may be made without departing from the scope and spirit of the invention. For example, the drives for plates 2, 3 and 4, 5 have been shown as being balanced arrangements wherein both plates are used for pickoff and for driving. Alternately, one plate could be used for pickoff and the other plate for driving. In addition, the specific arrangement shown for the balanced bridges coupled to plates 2-5 may be other than as shown, it being understood that the present circuitry employing inductors and capacitors is only by way of example. Furthermore, the present technique for separating the L signal into its components by using a demodulator and then remodulating the signal may be replaced with other known arrangements which do not employ demodulators and modulators. Also, it will be understood by those skilled in the art that the pickofis and drives need not be electrostatic, as shown. Numerous other arrangements are known for sensing motion and applying force. Finally, although the present invention has been described with respect to a string which is secured at opposite ends thereof, it will be apparent to those skilled in the art that it is also applicable to other types of vibrating members such as symmetrical bars supported at their nodes and whiskers of the type described in the above-mentioned patent application. Accordingly, it is to be understood that the invention is not to be limited by the specific illustrative embodiments disclosed, but only by the scope of the appended claims.

I claim:

1. Inertial reference apparatus comprising, in combination:

a string secured at opposite ends thereof;

means for driving said string in a first direction so as to cause said string to vibrate;

means for sensing motion of said string in a second direction which is substantially perpendicular to said first direction, said sensing means including means for detecting any elliptical component of the motion of said string;

means coupled to said sensing means to be responsive to motion in said second direction for producing a transverse force in said second direction, said transverse force including a component which is in-phase with displacement of the vibrating string in said first direction so as to reduce any elliptical component of the motion of said string.

2. The inertial reference apparatus of claim 1 wherein at least another component of said motion in'said second direction results from the direction of vibration of said string being angularly displaced relative to said first direction and wherein said means for driving said string as a function of said motion is operative to vibrate said string so that the vector sum of said drives coincides with said direction of vibration.

3. Inertial reference apparatus comprising, in combination:

a string secured at opposite ends thereof;

means for driving said string in a first direction so as to cause said string to vibrate;

means for sensing motion of said string in a second direction which is substantially perpendicular to said first direction wherein at least a portion of said motion in said second direction results from the direction of vibration of said string being displaced relative to said first direction; and

means for driving said string as a function of said sensed motion, said driving means being operative to vibrate said string so that the vector sum of said drives coincides with said direction of vibration.

4. Inertial reference apparatus comprising, in combination:

a string secured at opposite ends thereof;

means for driving said string in a first direction so as to cause said string to vibrate;

means for sensing motion of said string in a seconddirection which is substantially perpendicular to said first direction;

said means for sensing motion comprising a pair of electrostatic plates located on opposite sides of said string and perpendicular to said second direction;

a bridge circuit coupled to said pair of plates, two of the legs of said bridge circuit being formed by the capacitance between said string and each of said plates whereby motion of said string in said second direction unbalances said bridge; and

means for providing a signal which varies as a function of said bridge unbalance; and

means for driving said string as a function of said signal.

5. The inertial reference apparatus of claim 4 wherein at least a portion of said motion in said second direction results from said string vibrating in an elliptical path and wherein said means for driving said string as a function of said motion comprises:

means responsive to said bridge unbalance signal for extracting the component thereof due to said string vibrating in an elliptical path; and

means responsive to said elliptical path component for supplying a signal to said pair of electrostatic plates to force said string so as to minimize the minor axis of said elliptical path.

6. The inertial reference apparatus of claim 5 wherein said means for extracting said elliptical path component comprises:

a demodulator responsive to said bridge unbalance signal and adapted to receive, as a demodulating signal, a signal which is 90 out of phase with the motion of said string.

7. The inertial reference apparatus of claim 6 wherein said means for supplying a signal to said pair of plates comprises:

a modulator adapted to receive a signal which varies in accordance with the position of said string and adapted to receive, as a modulating signal, the output of said demodulator; and

circuit means operatively coupled to said modulator for applying the output therefrom to said plates.

8. The inertial reference apparatus of claim 4 wherein at least a portion of said motion in said second direction results from the direction of vibration of said string being displaced relative to said first direction and wherein said means for driving said string as a function of said motion comprises:

means responsive to said bridge unbalance signal for extracting the component thereof due to the direction of vibration of said string; and

means responsive to said direction of vibration component for supplying a signal to said pair of electrostatic plates so that the vector sum of said drives coincides with said direction of vibration.

9. The inertial reference apparatus of claim 8 wherein said means for extracting said direction of vibration component comprises:

a demodulator responsive to said bridge unbalance signal and adapted to receive, as a demodulating signal, a signal which varies in accordance with the position of said string.

10. The inertial reference apparatus of claim 9 wherein said means for supplying a signal to said pair of plates comprises:

a modulator adapted to receive a signal which is inphase with the velocity of said string and adapted to receive, as a modulating signal, the output of said demodulator; and

circuit means operatively coupled to said modulator for applying the output therefrom to said plates.

11. Inertial reference apparatus comprising, in combination:

a member having a longitudinal axis;

means for supporting said member at one point along said longitudinal axis;

means for driving said member in a first direction so as to cause said member to vibrate;

means for sensing motion of said member in a second direction which is substantially perpendicular to said first direction, said sensing means including means for detecting the elliptical component of the motion of said member;

means coupled to said sensing means to be responsive to motion in said second direction for producing a transverse force in said second direction,

said transverse force including a component which is in-phase with displacement motion of the vibrating member in said first direction so as to reduce any elliptical component of the motion of said member.

12. The inertial reference apparatus of claim 11 wherein said means for supporting said member is operative to support said member at two points along said longitudinal axis.

13. Inertial reference apparatus comprising, in combination:

a member having a longitudinal axis;

means for supporting said member at one point along said longitudinal axis;

means for driving said member in a first direction so as to cause said member to vibrate;

means for sensing motion of said member in a second direction which is substantially perpendicular to said first direction wherein at least a portion of said motion in said second direction results from the direction of vibration of said member being displaced relative to said first direction; and

means for driving said member as a function of said sensed motion, said driving means being operative to vibrate said member so that the vector sum of said drives coincides with said direction of vibration.

14. Inertial reference apparatus comprising, in combination:

an elongated member capable of being vibrated to provide an inertial reference in the direction of motion;

means causing said member to vibrate in said direction and having a displacement movement in said direction of motion;

compensation means including means for detecting any elliptical motion of said member to provide an out- 1 1 put which is a function of the transverse component causing said elliptical motion; and

means coupled to said output and responsive thereto for causing a transverse force to be produced on said member, said transverse force having a component which is in-phase with the displacement movement of the vibrating member in said first direction to minimize any transverse component producing said elliptical motion of said member.

15. In inertial reference apparatus including a member and driving force for vibrating said member in a reference plane, the combination comprising:

sensing means capable of sensing transverse motion of said member including combined in-phase and quadrature components; and

detector means for selectively detecting the in-phase and quadrature components of said lateral motion, said detector means includes means for separately amplifying said quadrative component at high gain,

means coupled to said amplifying means to produce a force component on said vibrating member normal to said reference plane for minimizing elliptical motion of said vibrating member.

16. The combination of claim 15 in Which said detector means further includes means for amplifying the in-phase component and producing a force component normal to said reference plane to compensate for movement of the reference plane relative to the driving force for vibrating said member.

17. The method of providing an inertial reference by vibration of an elongated member which method comprises:

producing stable vibratory motion of said member in a first direction of inertial reference;

detecting the magnitude of transverse movement of said member relative to said first direction; and

producing a transverse force varying in magnitude according to the magnitude of any detected transverse movement, said force having a phase such as to decrease the amplitude of any elliptical motion of said elongated member and applying said transverse force directly to said member.

18. The method of minimizing elliptical motion of an elongated member vibrating essentially in a nominal plane which method comprises:

detecting transverse motion out of the nominal plane of vibration of said vibrating member;

separating at least a substantial portion of the in-phase and quadrature components of said transverse motion; and

applying a force varying in magnitude according to the magnitude of said quadrature component to said member to minimize said quadrature component.

19. The method of claim 18 in which the quadrature component is operated on to produce a negative feedback for producing said force.

References Cited UNITED STATES PATENTS 2,552,650 5/1951 Rawlings 73 505 XR 3,047,766 7/1962 Glass. 3,106,847 10/1963 Mullins et al 73-505 JAMES I GILL, Primary Examiner 

